Right Angle / Right Triangle Calculator
Enter any two sides to solve for the missing side, or enter all three to check whether your triangle forms a right angle.
Tip: Use positive values only. If you enter all three sides, the calculator checks if a2 + b2 = c2.
What is a right angle?
A right angle is an angle that measures exactly 90 degrees. In geometry, a triangle with one right angle is called a right triangle. The side opposite the right angle is the hypotenuse, and it is always the longest side.
Right angles show up everywhere: building corners, stairs, framing, tile work, ramps, and even navigation. A fast right angle calculator helps you avoid manual errors and speed up planning.
How this right angle calculator works
This tool uses the Pythagorean theorem:
- a2 + b2 = c2
- a and b are the legs (the sides that form the 90° corner)
- c is the hypotenuse (the side across from the 90° angle)
Depending on what you enter, the calculator does one of two things:
- Two sides entered: computes the missing side.
- Three sides entered: verifies whether the values form a right triangle.
Common use cases
1) Construction and carpentry
Need to square a frame? Use a known ratio like 3-4-5 or scale it to 6-8-10. If your measured diagonal matches the computed hypotenuse, your corner is square.
2) DIY home projects
From installing shelves to planning deck posts, accurate right angles prevent crooked layouts and wasted material.
3) Surveying and land measurement
Right triangle checks are useful for determining distances where direct measurement is hard.
4) Math learning and exam prep
Students can quickly verify homework results and develop intuition for how side lengths relate in right triangles.
Worked examples
Example A: Find hypotenuse
Given legs a = 9 and b = 12:
c = √(92 + 122) = √(81 + 144) = √225 = 15.
Example B: Find a missing leg
Given hypotenuse c = 13 and leg a = 5:
b = √(132 - 52) = √(169 - 25) = √144 = 12.
Example C: Validate a triangle
Given sides 8, 15, and 17:
82 + 152 = 64 + 225 = 289, and 172 = 289, so this is a right triangle.
Tips for accurate results
- Use consistent units (all inches, all feet, all meters, etc.).
- Do not enter zero or negative values.
- For missing leg calculations, the hypotenuse must be larger than either leg.
- If field measurements are imperfect, tiny differences may come from rounding or tape-measure tolerance.
Right angle calculator FAQ
Can I use decimals?
Yes. Decimal values are fully supported.
Does this calculator find angles too?
This tool focuses on side relationships for right triangles. Once side lengths are known, trigonometric functions (sin, cos, tan) can be used to find non-right angles.
What if my three sides are close but not exact?
Real-world measurements often include slight error. If your values are very close, adjust for rounding and measurement precision before final cuts or installations.
Final thoughts
A right angle calculator is one of the most practical geometry tools you can use. It is quick, reliable, and useful in school, engineering, and hands-on building work. Enter your values above and get instant results for planning, checking, and problem-solving.